Is Rainwater Cleaner Than Tap Water?

It depends what stage of rainwater you are speaking about. At the exact microsecond moment a water bead forms, in the clouds it is indeed pure water in theory is “cleaner” than tap water. However in the exact microsecond after being created the rain drop begins voraciously absorbing every contaminant available to its surface, and the water begins degrading.
CO2 in the atmosphere is absorbed and quickly forms carbonic acid. Any atmospheric gasses, poisons and toxins are likewise absorbed. If there are metals, algae, bacteria or other organisms in the atmosphere the droplet will absorb those before reaching the earth’s surface where we would catch it.
In a pinch, in the wilderness drinking rainwater is the preferred alternative to dying of thirst, however rainwater will not pass the analytical specifications set in place by the Clean Water Drinking Act enforced by our EPA standards.
And remember, as with any water sample that does not contain chlorine, as the water sits it immediately allows bacteria, viruses, algae and other organisms to begin growing in it.